One possible extension is to add a label to each table. If each table has a label, we can restrict the use of tables by a sequence of labels, in which these tables must be applied. That means, if we have a set of tables $t_1, \dots, t_n$ and a control word $w = t_{i_1}, \dots, t_{i_k}$ for $i_j \in \{t_1, \dots, t_n\}$ the first table that must be applied is the table $t_{i_1}$. In the next step the table $t_{i_2}$ must be applied until in the last step, the table $t_{i_k}$ is applied. The last character in the control word must be the label of a terminal table. 

If we restrict the set of control words by the limitations within the Chomsky hierarchy, we obtain another class of language:

\begin{definition}
	$G' = (G, C)$ is a \emph{labelled TXMG with Y control} (for $X, Y \in \{R, CF, CS\}$) where
	\begin{compactitem}
		\item G is a $TXMG$, where each table has a label from $L$ and
		\item C is a Y control language, where $C \subset L^*$ 
	\end{compactitem} 
\end{definition}
We will abbreviate these type of grammars as $(Y)TXMG$. 

To underline the principle of these languages and their derivations, we will continue with an example:

\begin{example}
Let $G_{control} = (G, C)$ be a tabled matrix grammar with control with intermediates $\{S_1, S_2, S_3\}$ and $G = (G_H, G_V)$ where
\begin{compactitem}
	\item $L(G_H) = \{S_1^nS_2^nS_3^n \vert n \geq 1\}$, 
	\item the tables for $G_V$ are:
	\begin{compactitem}
		\item $t_1 = \{S_1 \rightarrow .S_1, S_2 \rightarrow xS_2, S_3 \rightarrow +S_3\}$,
		\item $t_2 = \{S_1 \rightarrow xS_1, S_2 \rightarrow xS_2, S_3 \rightarrow +S_3\}$ and
		\item $t_3 = \{S_1 \rightarrow +S_1, S_2 \rightarrow +S_2, S_3 \rightarrow +S_3\}$
		\item $t_4 = \{S_1 \rightarrow +, S_2 \rightarrow +, S_3 \rightarrow +\}$ and
	\end{compactitem}
	\item $C = \{t_1^mt_2^mt_3^mt_4 \vert m \geq 1\}$
\end{compactitem}
\end{example}

Due to the fact that $G_H$ is a context-sensitive grammar and $C$ is a context-sensitive language, the grammar $G_{control}$ is a (CS)TCSMG. 

This grammar generates pictures of size $(3n + 1, 3m)$ for $n, m \geq 1$. During the horizontal process $S_1^mS_2^mS_3^m$ is generated. $S_1$, $S_2$ and $S_3$ will be replaced by ., x and + while vertical derivation where $S_1$ is replaced by $.$, $S_2$ is replaced by $x$ and $S_3$ is replaced by $+$. The downward derivation repeats the same line than the first for $n$ times. Afterwards, $n$ lines are generated equally to the first one except that the .'s are replaced by x's. This is followed by $n + 1$ lines consisting only of +'s and then the derivation stops. To make this principle clear to the reader, we continue with an example picture of size $(4, 3)$: 

\[
\boxed{
\begin{aligned}
\begin{matrix}
S_1 & S_2 & S_3
\end{matrix}
\end{aligned}
}
\overset{t_1}{\underset{G_V}{\Downarrow}}
\boxed{
\begin{aligned}
\begin{matrix}
. & x & + \\[-0.5ex]
S_1 & S_2 & S_3
\end{matrix}
\end{aligned}
}
\overset{t_2}{\underset{G_V}{\Downarrow}}
\boxed{
\begin{aligned}
\begin{matrix}
. & x & + \\[-0.5ex]
x & x & + \\[-0.5ex]
S_1 & S_2 & S_3
\end{matrix}
\end{aligned}
}
\overset{t_3}{\underset{G_V}{\Downarrow}}
\boxed{
\begin{aligned}
\begin{matrix}
. & x & + \\[-0.5ex]
x & x & + \\[-0.5ex]
+ & + & + \\[-0.5ex]
S_1 & S_2 & S_3
\end{matrix}
\end{aligned}
}
\overset{t_4}{\underset{G_V}{\Downarrow}}
\boxed{
\begin{aligned}
\begin{matrix}
. & x & + \\[-0.5ex]
x & x & + \\[-0.5ex]
+ & + & + \\[-0.5ex]
+ & + & +
\end{matrix}
\end{aligned}
}
\]

This description is only an excerpt from~\cite{sironmoney1977parallelsequential}. The following theorem is also from~\cite{sironmoney1977parallelsequential} and originally included some more subclasses. A description of those would go beyond the scope of this paper. 

\begin{theorem}
\begin{align*}
TXML = (R)TXML
\end{align*}
\end{theorem}